Techniques for analyzing characteristics of an electronic device such as a transistor have been known. For example, a technique for analyzing characteristics of a MOS transistor is disclosed in a non-patent literature 1.
FIG. 1 is a sectional view showing a configuration of a model transistor described in the non-patent literature 1. A MOS transistor 150 as a model transistor includes a gate electrode 151, a gate oxide film 152, a drain region 153, a channel region 154 and a source region 155. The channel region 154 is formed between the source region 155 and the drain region 153 below the gate electrode 151 and the gate oxide film 152. In the non-patent literature 1, the channel region 154 is divided into three regions, and widths and impurity concentrations of the respective regions are calculated as model parameters to perform analysis and design of a semiconductor device by using the model parameters.
Here, it is supposed that respective widths of the three channel regions in a channel direction are represented as L1, L2, and L1 and impurity concentrations thereof are represented as Np, Nc, and Np. Temporary setting is performed to coincide with a channel impurity concentration distribution in an actual transistor excellently by using L1, L2, Np, and Nc as the model parameters. Next, regarding each of the channel regions, a surface potential thereof is determined by solving a Poisson equation using the surface potential as a variable. Subsequently, electric characteristics of the transistor are calculated by using the determined surface potentials.
The electric characteristics of the transistor are exemplified as gate capacity Cgg—gate voltage Vc characteristic and threshold voltage Vth—substrate voltage VB characteristic (or drain current ID—substrate voltage VBb characteristic). As a method of calculating these electric characteristics of the transistor, a method described in the non-patent literature 1 or a method conventionally known widely can be used. Here, when the determined electric characteristic of the transistor (calculation values) do not coincide with electric characteristics of an actual transistor (measurement values), the above-mentioned calculation is repeated while the temporarily set model parameters L1, L2, Np, and Nc are changed. On the other hand, when the calculation values coincide with the measurement values, it is thought that the temporarily set model parameters L1, L2, Np, and Nc represent the channel impurity concentration distribution of the actual transistor. Thus, analysis or design of a semiconductor device is performed by using the determined model parameters.
It should be noted that the method of calculating electric characteristics of a transistor is described in non-patent literature 2.